{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Parametric plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When looking at Riemann problems, it is common to think about how a *wave* connects a *state* that is known to other states. For example, the Hugoniot curve gives the set of states that can be connected to a known state by a shock. Solutions to Riemann problems can be illustrated by the intersections of such curves in some parametric space.\n", "\n", "Here we will illustrate this by showing how the curves for various problems behave in the pressure-velocity ($P-v$) space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Inert case" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from r3d2 import eos_defns, State, RiemannProblem, utils\n", "from matplotlib import pyplot\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "gamma = 5.0/3.0\n", "eos = eos_defns.eos_gamma_law(gamma)\n", "test_1_U_left = State(10.0, 0.0, 0.0, 2.0, eos, label=\"L\")\n", "test_1_U_right = State(1.0, 0.0, 0.0, 0.5, eos, label=\"R\")\n", "\n", "test_1_rp = RiemannProblem(test_1_U_left, test_1_U_right)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This Riemann problem has a simple rarefaction-shock structure: a left going rarefaction, a contact, and a right going shock." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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sEypJsqrSuXNnXnzxRS5KYzb43377jbZt23oH6tWqVYvRo0fbQL0sJCKFROQD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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import display, display_png\n", "display_png(test_1_rp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution in parameter space shows the curves that can connect to the left and right states. Both a shock and a rarefaction can connect to either state. However, the only intersection (for the central, \"star\" state) is when a left going rarefaction connects to the left state, and a right going shock connects to the right state:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/ih3/anaconda/lib/python3.4/site-packages/scipy/integrate/odepack.py:218: ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information.\n", " warnings.warn(warning_msg, ODEintWarning)\n" ] }, { "data": { "image/png": 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bWbJkSbVfl5ubS1lZGa1bt671a55IhVREJAx06eI6gYj/bczP5+EwHSH1pUjW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\nBJdeCqmp0L2760TBaWtBAc+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JSy+9RMeOHQF4/fXXueqqq4ipuP7SYy1ZpaXVls3M0lLa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\nwKofNxXrI8DOmZkAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = pyplot.figure(figsize=(10,6))\n", "ax = fig.add_subplot(111)\n", "utils.plot_P_v(test_1_rp, ax, fig)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Varying EOS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As noted previously, it's not necessary for the equation of state to match in the different states. Here is a problem with two inert EOSs. This problem is solved by two rarefactions." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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p0qxdu5aoqCi8vb25cuUKXl5eTJkyRfshp5AUrFq9rpQKUUodVkodU0p1Mef4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\n2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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "gamma_air = 1.4\n", "eos_air = eos_defns.eos_gamma_law(gamma_air)\n", "U_vary_eos_L = State(1.0, -0.5, 0.0, 2.0, eos, label=\"L\")\n", "U_vary_eos_R = State(1.0, +0.5, 0.0, 2.0, eos_air, label=\"R\")\n", "test_vary_eos_rp = RiemannProblem(U_vary_eos_L, U_vary_eos_R)\n", "display_png(test_vary_eos_rp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parametric solution in this case shows the pressure decreasing across both curves along rarefactions to get to the star state:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LFsEHH0DZhD1JUha5d84cCpct47lNCgdln1wuTmvCL3/5S6644gpatmz5tfcs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\nShm3Zg2cdRY8+2zSSSTVAIt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig2 = pyplot.figure(figsize=(10,6))\n", "ax2 = fig2.add_subplot(111)\n", "utils.plot_P_v(test_vary_eos_rp, ax2, fig2)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Reactive cases" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once reactions start, the behaviour gets more complex, and the parametric pictures can clarify some aspects. An example would be a single deflagration wave that is preceded by a shock to ignite the reaction:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/ih3/anaconda/lib/python3.4/site-packages/scipy/integrate/odepack.py:218: ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information.\n", " warnings.warn(warning_msg, ODEintWarning)\n" ] }, { "data": { "image/png": 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rrriieDaMZ599lrVr13LxxReX6LbhyvWxmXUFDgPeBv6+FXU7Ah+Y2admthF4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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "eos = eos_defns.eos_gamma_law(5.0/3.0)\n", "eos_reactive = eos_defns.eos_gamma_law_react(5.0/3.0, 0.1, 1.0, 1.0, eos)\n", "U_reactive_right = State(0.5, 0.0, 0.0, 1.0, eos_reactive)\n", "U_reactive_left = State(0.24316548798524526, -0.39922932397353039, 0.0,\n", " 0.61686385086179807, eos)\n", "test_precursor_rp = RiemannProblem(U_reactive_left, U_reactive_right)\n", "display_png(test_precursor_rp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The structure here looks like previous Riemann problems, but there is in fact only one wave. The right state is connected directly to the left state across a compound wave formed from a precursor shock, which raises the temperature until the gas ignites, then a Chapman-Jouget deflagration which is attached to a rarefaction.\n", "\n", "In parameter space we see this behaviour more directly:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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uLlQk+95//32aNWuW9vrRRx+lb9++Xqzo2hRqRUREsstaZ0ewl16C//s/GDoU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\n0Z9TREREJDe0Ta6PS0lx/pvZpgZbtkC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig3 = pyplot.figure(figsize=(10,6))\n", "ax3 = fig3.add_subplot(111)\n", "utils.plot_P_v(test_precursor_rp, ax3, fig3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The smooth joining of the deflagration and rarefaction curves at the Chapman-Jouget (CJ) point is expected, as the propagation speed of the waves must match there. The ignition point (where the temperature is high enough for the reaction to take place) is illustrated by the \"$i$\"." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.4" } }, "nbformat": 4, "nbformat_minor": 0 }